Eighteen individuals are scheduled to take a driving test at a particular DMV office on a certain day, eight of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. (a) What kind of a distribution does X have (name and values of all parameters)? h(x; 6, 8, 18) 8 b(x; 6, 18 b(x; 6, 8, 18) nb(x; 6, 8, 18) 8 O h(x; 6, 18 8 nb(x; 6, 18 (b) Compute P(X = 2), P(X < 2), and P(X > 2). (Round your answers to four decimal places.) P(X = 2) %3D P(X < 2) %D P(X > 2) : (c) Calculate the mean value and standard deviation of X. (Round your answers to three decimal places.) mean individuals standard deviation individuals
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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